On the Strong Equitable Vertex 2-Arboricity of Complete Bipartite Graphs

Fangyun Tao, Ting Jin and Yiyou Tu
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Fangyun Tao: Department of Applied Mathematics, College of Science, Nanjing Forestry University, Nanjing 210037, China
Ting Jin: Department of Applied Mathematics, College of Science, Nanjing Forestry University, Nanjing 210037, China
Yiyou Tu: School of Materials Science and Engineering, Southeast University, Nanjing 211189, China

Mathematics, 2020, vol. 8, issue 10, 1-6

Abstract: An equitable partition of a graph G is a partition of the vertex set of G such that the sizes of any two parts differ by at most one. The strong equitable vertexk - arboricity of G , denoted by v a k ≡ ( G ) , is the smallest integer t such that G can be equitably partitioned into t ′ induced forests for every t ′ ≥ t , where the maximum degree of each induced forest is at most k . In this paper, we provide a general upper bound for v a 2 ≡ ( K n , n ) . Exact values are obtained in some special cases.

Keywords: combinatorial problems; equitable coloring; equitable partition; vertex arboricity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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